Game Object: localOrientation

[ cosine of the angle of the world X-axis to the game object x-axis,
cosine of the angle of the world X-axis to the game object y-axis,
cosine of the angle of the world X-axis to the game object z-axis ]

Y-axis vector:

[ cosine of the angle of the world Y-axis to the game object x-axis,
cosine of the angle of the world Y-axis to the game object y-axis,
cosine of the angle of the world Y-axis to the game object z-axis ]

Z-axis vector:

[ cosine of the angle of the world Z-axis to the game object x-axis,
cosine of the angle of the world Z-axis to the game object y-axis,
cosine of the angle of the world Z-axis to the game object z-axis ]

Example:

Game object axis orientation is the same as the world axis

Values:

Cosine of 90 degrees is 0.00

Cosine of 0 degrees is 1.00

World X-axis:

angle to game object x-axis = 0 degrees

angle to game object y-axis = 90 degrees

angle to game object z-axis = 90 degrees

World Y-axis:

angle to game object x-axis = 90 degrees

angle to game object y-axis = 0 degrees

angle to game object z-axis = 90 degrees

World Z-axis:

angle to game object x-axis = 90 degrees

angle to game object y-axis = 90 degrees

angle to game object z-axis = 0 degrees

3x3 Matrix:

[[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]]

Example:

Game object is rotated 45 degrees on the game object y-axis

Values:

Cosine of 90 degrees is 0.00

Cosine of 0 degrees is 1.00

Cosine of 45 degrees is 0.7071

Cosine of 135 degrees is -0.7071

World X-axis:

angle to game object x-axis = 45 degrees

angle to game object y-axis = 90 degrees

angle to game objcet z-axis = 45 degrees

World Y-axis:

angle to game object x-axis = 90 degrees

angle to game object y-axis = 0 degrees

angle to game object z-axis = 90 degrees

World Z-axis:

angle to game object x-axis = 135 degrees

angle to game object y-axis = 90 degrees

angle to game object z-axis = 45 degrees

3x3 Matrix:

[[0.7071, 0.0, 0.7071], [0.0, 1.0, 0.0], [-0.7071, 0.0, 0.7071]]

Note:

Game object not parented:

Local orientation is the orientation using the world axis as it's starting point

Game object parented:

Local orientation is the orientation using the parent's axis as it's starting point